As a generalization of graphs, hypergraphs are widely used to model
higher-order relations in data. This paper explores the benefit of the
hypergraph structure for the interpolation of point cloud data that contain no
explicit structural information. We define the $\varepsilon_n$-ball hypergraph
and the $k_n$-nearest neighbor hypergraph on a point cloud and study the
$p$-Laplacian regularization on the hypergraphs. We prove the variational
consistency between the hypergraph $p$-Laplacian regularization and the
continuum $p$-Laplacian regularization in a semisupervised setting when the
number of points $n$ goes to infinity while the number of labeled points
remains fixed. A key improvement compared to the graph case is that the results
rely on weaker assumptions on the upper bound of $\varepsilon_n$ and $k_n$. To
solve the convex but non-differentiable large-scale optimization problem, we
utilize the stochastic primal-dual hybrid gradient algorithm. Numerical
experiments on data interpolation verify that the hypergraph $p$-Laplacian
regularization outperforms the graph $p$-Laplacian regularization in preventing
the development of spikes at the labeled points.

探索了超图结构在不包含显式结构信息的点云数据插值中的优势，并证明了超图 $p$-Laplacian 正则化与连续型 $p$-Laplacian 正则化的变分一致性，利用随机原始 - 对偶混合梯度算法解决了凸但不可微的大规模优化问题，并通过数值实验验证了超图 $p$-Laplacian 正则化相对于图 $p$-Laplacian 正则化在防止标记点处出现尖峰的效果更好。

点云数据插值上的超图 p-Laplace 正则化

Hypergraph $p$-Laplacian regularization on point clouds for data  interpolation

Crime has become a major concern in many cities, which calls for the rising
demand for timely predicting citywide crime occurrence. Accurate crime
prediction results are vital for the beforehand decision-making of government
to alleviate the increasing concern about the public safety. While many efforts
have been devoted to proposing various spatial-temporal forecasting techniques
to explore dependence across locations and time periods, most of them follow a
supervised learning manner, which limits their spatial-temporal representation
ability on sparse crime data. Inspired by the recent success in self-supervised
learning, this work proposes a Spatial-Temporal Hypergraph Self-Supervised
Learning framework (ST-HSL) to tackle the label scarcity issue in crime
prediction. Specifically, we propose the cross-region hypergraph structure
learning to encode region-wise crime dependency under the entire urban space.
Furthermore, we design the dual-stage self-supervised learning paradigm, to not
only jointly capture local- and global-level spatial-temporal crime patterns,
but also supplement the sparse crime representation by augmenting region
self-discrimination. We perform extensive experiments on two real-life crime
datasets. Evaluation results show that our ST-HSL significantly outperforms
state-of-the-art baselines. Further analysis provides insights into the
superiority of our ST-HSL method in the representation of spatial-temporal
crime patterns. The implementation code is available at
this https URL.

提出了一种基于超图自监督学习的空间 - 时间犯罪预测框架，用于解决标签稀缺问题，并在两个真实犯罪数据集上得到了显着优于现有基线的评估结果。

基于时空超图自监督学习的犯罪预测

Spatial-Temporal Hypergraph Self-Supervised Learning for Crime Prediction

The application of deep reinforcement learning in multi-agent systems
introduces extra challenges. In a scenario with numerous agents, one of the
most important concerns currently being addressed is how to develop sufficient
collaboration between diverse agents. To address this problem, we consider the
form of agent interaction based on neighborhood and propose a multi-agent
reinforcement learning (MARL) algorithm based on the actor-critic method, which
can adaptively construct the hypergraph structure representing the agent
interaction and further implement effective information extraction and
representation learning through hypergraph convolution networks, leading to
effective cooperation. Based on different hypergraph generation methods, we
present two variants: Actor Hypergraph Convolutional Critic Network (HGAC) and
Actor Attention Hypergraph Critic Network (ATT-HGAC). Experiments with
different settings demonstrate the advantages of our approach over other
existing methods.

本文介绍了一种基于邻域的多智能体强化学习算法，并提出了两种基于超图结构的变体方法，其中利用超图卷积网络实现了信息提取和表示学习，具有实现有效合作的显著优势。

基于超图神经网络的多智能体系统高效策略生成

Efficient Policy Generation in Multi-Agent Systems via Hypergraph Neural Network

Cross-platform account matching plays a significant role in social network
analytics, and is beneficial for a wide range of applications. However,
existing methods either heavily rely on high-quality user generated content
(including user profiles) or suffer from data insufficiency problem if only
focusing on network topology, which brings researchers into an insoluble
dilemma of model selection. In this paper, to address this problem, we propose
a novel framework that considers multi-level graph convolutions on both local
network structure and hypergraph structure in a unified manner. The proposed
method overcomes data insufficiency problem of existing work and does not
necessarily rely on user demographic information. Moreover, to adapt the
proposed method to be capable of handling large-scale social networks, we
propose a two-phase space reconciliation mechanism to align the embedding
spaces in both network partitioning based parallel training and account
matching across different social networks. Extensive experiments have been
conducted on two large-scale real-life social networks. The experimental
results demonstrate that the proposed method outperforms the state-of-the-art
models with a big margin.

本文提出了一种基于多层图卷积的新框架，以解决现有方法在跨平台账户匹配方面存在的数据不足问题，并能够处理大规模社交网络。